Unfortunately that solution will not work for me, as the device is not designed to be used near a router. I am just trying to find a way, other than BlueTooth (if possible) to create a connection between two devices, one being the Arduino. I don't need internet access. I guess WiFi is probably overkill for what I am trying to achieve. Maybe I should just face the fact that I will need to stick with BlueTooth.
No, WiFi is not overkill. It may have much more data transfer rate than you need, however it is ubiquitous and nearly all mobile phones, tablets, laptops etc. can easily connect to it.
Bluetooth on the other hand is much less power hungry than WiFi.
If power in not a problem than you still should be able to connect the Ethernet card to a little Pocket router such as the TP- Link WR703n or WR702n. These accept 5V USB power and you can run them off of the Arduino. Not only is that likely less expensive than a WiFi shield but also probably works better. The TP link can work as its own AP, so you can connect directly to it without the use of another router.
I've done it in two projects and it works flawlessly.